A User Equipment (UE), also known as a mobile station, wireless terminal and/or mobile terminal is enabled to communicate wirelessly in a wireless communication system, sometimes also referred to as a cellular radio system or a wireless communication network. The communication may be made, e.g., between UEs, between a UE and a wire connected telephone and/or between a UE and a server via a Radio Access Network (RAN) and possibly one or more core networks. The wireless communication may comprise various communication services such as voice, messaging, packet data, video, broadcast, etc.
The UE may further be referred to as mobile telephone, cellular telephone, computer tablet or laptop with wireless capability, etc. The UE in the present context may be, for example, portable, pocket-storable, hand-held, computer-comprised, or vehicle-mounted mobile devices, enabled to communicate voice and/or data, via the radio access network, with another entity, such as another UE or a server.
The wireless communication system covers a geographical area which is divided into cell areas, with each cell area being served by a radio network node, or base station, e.g., a Radio Base Station (RBS) or Base Transceiver Station (BTS), which in some networks may be referred to as “eNB”, “eNodeB”, “NodeB” or “B node”, depending on the technology and/or terminology used.
Sometimes, the expression “cell” may be used for denoting the radio network node itself. However, the cell may also in normal terminology be used for the geographical area where radio coverage is provided by the radio network node at a base station site. One radio network node, situated on the base station site, may serve one or several cells. The radio network nodes may communicate over the air interface operating on radio frequencies with any UE within range of the respective radio network node.
In some radio access networks, several radio network nodes may be connected, e.g., by landlines or microwave, to a Radio Network Controller (RNC), e.g., in Universal Mobile Telecommunications System (UMTS). The RNC, also sometimes termed Base Station Controller (BSC), e.g., in GSM, may supervise and coordinate various activities of the plural radio network nodes connected thereto. GSM is an abbreviation for Global System for Mobile Communications (originally: Groupe Spécial Mobile).
In 3rd Generation Partnership Project (3GPP) Long Term Evolution (LTE) radio network nodes, which may be referred to as eNodeBs or eNBs, may be connected to a gateway, e.g., a radio access gateway, to one or more core networks.
In the present context, the expressions downlink, downstream link or forward link may be used for the transmission path from the radio network node to the UE. The expression uplink, upstream link or reverse link may be used for the transmission path in the opposite direction, i.e., from the UE to the radio network node.
Orthogonal Frequency Division Multiplexing (OFDM) is the dominant modulation technique in contemporary systems such as LTE and WIFI. OFDM is a method of encoding digital data on multiple carrier frequencies. OFDM is a Frequency-Division Multiplexing (FDM) scheme used as a digital multi-carrier modulation method. A large number of closely spaced orthogonal sub-carrier signals are used to carry data. The data is divided into several parallel data streams or channels, one for each sub-carrier.
A common, and severe, problem of OFDM is frequency offset between the transmitting part and the receiving part. This is herein referred to as Carrier Frequency Offset (CFO). A CFO implies that the transmitter and the receiver are mis-aligned with each other and the effect of this is that orthogonality among the OFDM sub-carriers is lost. As orthogonality among sub-carriers is the whole point of OFDM, this situation is unacceptable and counter-measures must be taken. In the case that the CFO would be known to the receiver, it can simply compensate for the CFO by a frequency shift, and orthogonality is assured. Hence, mitigating CFOs is equivalent to the problem of estimating the CFO from the received data.
The CFO is usually broken up into two parts, the Integer Frequency Offset (IFO) and the Fractional Frequency Offset (FF0):εCFO=εIFO+εFFO where εIFO is an integer multiplied by the sub-carrier spacing and εFF0 is limited in magnitude to half the sub-carrier spacing. In LTE, the sub-carrier spacing is 15 kHz, so the FFO is limited to 7.5 kHz in magnitude, and the IFO can be . . . , −30 kHz, −15 kHz, 0, 15 kHz, 30 kHz, . . .
During initial synchronization, the precise value of εIFO is obtained. Hence, the remaining task is to estimate the FFO. Throughout this disclosure, it is assumed that the IFO has already been estimated, e.g. during initial synchronization. It is standard notational procedure to normalize all offsets by the subcarrier spacing, so that the FFO is limited to εFFO∈[−½,½]and:εIFO ∈{. . . ,−3,−2,−1, 0, 1, 2, 3, . . . }.
The FFO must be estimated based on the received signals. It is herein assumed that two OFDM symbols are available. A condition for enabling calibration to work is that these two symbols comprise training symbols, a.k.a., pilot symbols. If so, then based on these two OFDM symbols it is desired to have a (near)-optimal FFO estimator algorithm capable of dealing with an arbitrary FFO in the range εFFO∈[−½, ½].
A system model will subsequently be described. Let sr1 and sr2 denote the received OFDM symbols at time r1 and r2, respectively. Further, it may be assumed that time synchronisation and IFO compensation have been carried out so that the Cyclic Prefix (CP) has been removed from the two symbols and the CFO is at most 0.5 in magnitude (i.e., only the FFO remains). Let {tilde over (s)}r1 and {tilde over (s)}r2 denote the two signals in the case of no FFO at all. Then: sk=Dk(εFF0){tilde over (s)}k, k∈{r1, r2}, where Dk(εFFO) is the diagonal matrix:
            D      k        ⁡          (              ɛ        FFO            )        =      diag    ⁢                  {                  exp          (                      2            ⁢                                                  ⁢            π            ⁢                                                  ⁢            i            ⁢                                                  ⁢                                          ɛ                FFO                            ⁡                              [                                                                            n                      -                      1                                                              N                      FFT                                                        +                                      k                    ⁢                                                                                  ⁢                    Δ                                                  ]                                              )                }                    n        =        1                    N        FFT            Where NFFT is the FFT-size and Δ is the separation of the two symbols sr1 and sr2 measured in units of one OFDM symbol length including the Cyclic Prefix.
Example: when the Cyclic Prefix is NCP samples long, then:Δ=(r2−r1)(NFFT+NCP)/NFFT.Let Q denote the Discrete Fourier Transform (DFT) matrix of size NFFT. Thus QDkH(εFF0)sk=Hkxk, where Hk is a diagonal matrix comprising the frequency response of the channel along its main diagonal and xk is a column vector with the transmitted frequency symbols. The vector xk, comprises both training symbols and payload data. Let γk denote the set of positions of xk that are allocated to training symbols. Also, xk=pk+dk where p k is the vector of training symbols satisfying Pk[l]=0,l∉γk, i.e., there is no training symbols at the data positions, and dk are the data symbols satisfying dk[l]=0,l∈γk, i.e., there is no data at the training positions. It may be assumed that the pilot positions are not dependent on the OFDM symbol index, hence γr=γt=γ.
The problem of FFO estimation is well known and has a long and rich history. There are two main branches for FFO estimation: (1) time-domain approaches and (2) frequency domain approaches.
In the time-domain approach, the redundancy added in the Cyclic Prefix, is utilised. Several disadvantages are however associated with this approach such as e.g. that the estimators suffer from problems with DC offsets, spurs and narrow band interferences.
When describing a periodic function in the frequency domain, DC offset, or the DC bias/DC component/DC coefficient as it also may be referred to, is the mean value of the waveform. If the mean amplitude is zero, there is no DC offset.
Within the frequency domain approaches, the baseline method is to make the approximation:Zk=Qsk≈exp(i2πεFFOΔ)Hkxk that is, after the FFT, the FFO shows up multiplicatively at each sub-carrier.
Thermal noise on the observations has here been omitted. At the positions specified in the pilot position set γ, the symbols in xk are known. Thereby, the FFO may be estimated as:
            ɛ      ^        FFO    =            1              2        ⁢                                  ⁢        π        ⁢                                  ⁢        Δ              ⁢    arg    ⁢                  {                              ∑                          l              ∈              Υ                                ⁢                                          ⁢                                                                      z                                      r                    ⁢                                                                                  ⁢                    1                                    H                                ⁡                                  [                  l                  ]                                                                              p                                      r                    ⁢                                                                                  ⁢                    1                                    H                                ⁡                                  [                  l                  ]                                                      ⁢                                                            z                                      r                    ⁢                                                                                  ⁢                    2                                                  ⁡                                  [                  l                  ]                                                                              p                                      r                    ⁢                                                                                  ⁢                    2                                                  ⁡                                  [                  l                  ]                                                                    }            .      
The baseline frequency based estimator however suffers from two main problems: (i) The approximation zk=Qsk≈exp(i2πεFFOΔ)Hkxk is only an approximation, and introduces additional noise into the system. It is not optimal in any sense, although complexity wise attractive.
The second (ii) problem is that it is limited to a maximal FFO of ½Δ. In LTE, a typical value for Δ may be approximately e.g. 3.21, which results from using OFDM symbol 4 and 7 within each sub-frame and using the normal CP. This means that the maximal FFO possible to detect is only |εFFO|<εmax=½Δ=0.1667≈2.33 kHz . This is far less than half the sub-carrier spacing of 7.5 kHz. As a remedy to the second problem, an extension of the baseline in order to extend the maximal FFO to 0.5-corresponding to 7.5 kHz in LTE may be made according to some prior art solutions. However, such solution comprises the use of more than two OFDM symbols in the FFO estimation. Further, the problem (i) is not dealt with and will ultimately limit the performance.
Yet another method to deal with the second (ii) problem is to use three identical copies of the baseline method in order to cover three times as large FFO interval. The first copy is shifted in frequency into 4.66 kHz, and the third copy is shifted to 4.66 kHz. The second copy is not shifted and is the normal baseline method. After the frequency shifts, an evaluation may be made:
            ɛ      ^        FFO    =            1              2        ⁢                                  ⁢        π        ⁢                                  ⁢        Δ              ⁢    arg    ⁢          {                        ∑                      l            ∈            Υ                          ⁢                                  ⁢                                                            z                                  r                  ⁢                                                                          ⁢                  1                                H                            ⁡                              [                l                ]                                                                    p                                  r                  ⁢                                                                          ⁢                  1                                H                            ⁡                              [                l                ]                                              ⁢                                                    z                                  r                  ⁢                                                                          ⁢                  2                                            ⁡                              [                l                ]                                                                    p                                  r                  ⁢                                                                          ⁢                  2                                            ⁡                              [                l                ]                                                        }      three times, once for each frequency shift. Then the final output is the estimate with maximal value of:
      ∑          l      ∈      Υ        ⁢          ⁢                              z                      r            ⁢                                                  ⁢            1                    H                ⁡                  [          l          ]                                      p                      r            ⁢                                                  ⁢            1                    H                ⁡                  [          l          ]                      ⁢                                        z                          r              ⁢                                                          ⁢              2                                ⁡                      [            l            ]                                                p                          r              ⁢                                                          ⁢              2                                ⁡                      [            l            ]                              .      
This algorithm may be referred to as “extended baseline”. However, this algorithm performs poorly, as it does not adequately address the problem (i).
Thus, there is room for improvement when estimating carrier frequency offset.